2015 AMC 12B Problem 4

Below is the professionally curated solution for Problem 4 of the 2015 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 12B solutions, or check the answer key.

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Concepts:logical deduction work backwards

Difficulty rating: 1130

David, Hikmet, Jack, Marta, Rand, and Todd were in a $12$ -person race with $6$ other people. Rand finished $6$ places ahead of Hikmet. Marta finished $1$ place behind Jack. David finished $2$ places behind Hikmet. Jack finished $2$ places behind Todd. Todd finished $1$ place behind Rand. Marta finished in $6$ th place. Who finished in $8$ th place?

David

Hikmet

Jack

Rand

Todd

Solution:

Marta is $6$ th, so Jack is $5$ th. Jack is $2$ behind Todd, so Todd is $3$ rd. Todd is $1$ behind Rand, so Rand is $2$ nd.

Rand is $6$ ahead of Hikmet, so Hikmet is $8$ th. (David is $10$ th.)

Thus, the correct answer is B.

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